LONDON—Diageo PLC said Tuesday it made a $1.9 billion offer to take control of India's United Spirits Ltd., the latest attempt by the U.K. liquor giant to forge a dominant position in the world's biggest whiskey market.

Diageo's open-market offer for an additional 26% stake in United Spirits was pegged at 3,030 rupees (about $50) a share. If the deal is successful, Diageo's total stake would rise to 54.78%, giving it...